The former Chief Financial Officer of BP has proven himself to be adept at cleaning up messes and firefighting, investors say.
Gilvary, 58, who retired from BP in June after 34 years including eight as finance chief, oversaw the oil giant's recovery from the catastrophic Deepwater Horizon oil spill which cost it $65 billion in fines and huge reputational damage.
Gilvary also led discussions with BP's top investors around the oil and gas company's commitment to reducing carbon emissions, which led to a 2019 shareholder resolution in which BP committed to align its strategy with the 2015 Paris climate agreement.
Still, the British oil executive has drawbacks: he has no mining industry experience, and although he has a good reputation for stakeholder management and relationships, he does not have experience in Australia.
Gilvary declined to comment when asked about his possible candidacy for the Rio job.
Pearce, 56, an Australian who was appointed as Anglo American's financial director in 2017, was previously an executive director and CFO at Australian iron ore miner Fortescue Metals Group.
He has also held senior positions in Australian engineering and oil and gas companies.
A chartered accountant, Pearce's years at Fortescue and Anglo American were marked by slashing debt while raising spending cautiously.
He has also been spoken of in the industry as a possible successor for Anglo American's CEO Mark Cutifani.
Pearce and Anglo American declined to comment.
The chief executive of Australian copper producer Oz Minerals, Cole spent 22 years at Rio Tinto and is well regarded by analysts and investors as a forward thinker and strong project manager.
A geophysicist by training, the 50-year-old Australian ran Rio's iron and titanium division out of Montreal, managed its China exploration joint venture and has worked on various projects around the world.
"Get the people and culture right, and the rest will take care of itself," he says on his LinkedIn profile.
Critics suggest that Cole, may not yet have the operational experience for the top job.
The 62-year-old former chief executive of Fortescue drove it to become the world's fourth-biggest producer of iron ore under his watch.
The charismatic Australian has built solid relationships in government, most recently chairing Australia's COVID-19 economic recovery plan.
The plan, which will rely on an expansion of Australia's natural gas to fuel manufacturing, has been criticised by some energy experts who favour renewables as a cleaner, more economic solution.
Candidates seen as long shots include Shell Australia chairman Zoe Yujnovich, who once ran Rio's Canadian iron ore business, and former AngloGold Ashanti boss Kelvin Dushnisky.
(Reporting by Melanie Burton in Melbourne and Helen Reid in Johannesberg; additional reporting by Ron Bousso, Ron Bousso, Zandi Shabalala and Clara Denina in London; editing by Richard Pullin)